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Question
Verify the division algorithm i.e. Dividend = Divisor × Quotient + Remainder, in each of the following. Also, write the quotient and remainder.
| Dividend | Divisor |
| 34x − 22x3 − 12x4 − 10x2 − 75 | 3x + 7 |
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Solution
Quotient = - 4x3 + 2x2 - 8x + 30
Remainder = - 285
Divisor = 3x + 7
Divisor x Quotient + Remainder = (3x + 7) (- 4x3 + 2x2 - 8x + 30) - 285
= 12x4 + 6x3 - 24x2 + 90x - 28x3 + 14x2 - 56x + 210 - 285
= - 12x 4 - 22x3 -10x2 + 34x - 75
= Dividend
Thus,
Divisor x Quotient + Remainder = Dividend
Hence verified.
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